President-elect Donald Trump signaled Thursday that he will look to "strengthen and expand" the US's nuclear capability hours after Russian President Vladimir Putin pledged to enhance his country's nuclear forces.

The exchange appeared to raise the prospect of a new arms race between the two nuclear superpowers, which between them boast more than 14,000 nuclear warheads, the still deadly legacy of their four-decades long Cold War standoff.

But the comments by Putin, who is presiding over a project to restore Russia's lost global power and influence, and Trump, who will shortly become the US commander-in-chief, did not spell out exactly what each side is proposing or whether a major change of nuclear doctrine is in the offing.